This is in continuance to my earlier post : Deriving expression for general cubic equation solution. Also, the links are repeated for the first four pages of the book by Dickson, titled "Introduction to Theory of Algebraic Equations" are given as : page #1,$\,$page #2,$\,$ page #3, $\,$page #4.$\,$ Added are rest $5$ pages (#$5$ to #$9$) from first chapter of the book : page #5, $\,$ page #6,$\,$ page #7,$\,$ page #8,$\,$ page #9.
On page $2$ of the book, the Hudde substitution ($y = z - \frac{p}{3z}$) specifically uses $p$, that stands for
$$p=c_2 -\frac{1}{3}c_1^2$$$$\implies y= z-\frac{(x_1x_2+x_2x_3+x_3x_1)-\frac{1}{3}(x_1+x_2+x_3)^2}{3z}$$$$\implies y = z -\frac{x_1(x_2-x_1)+x_3(x_1-x_3)+x_2(x_3-x_2)}{3z}$$$$\implies y = z +\frac{x_1(x_1-x_2)+x_3(x_3-x_1)+x_2(x_2-x_3)}{3z}$$ The book sidelines the issue, and am not aware of any source that gives details about its significance.
